Ms. Guidance to Xtra Dimensions

ARTICLES and DOCUMENTS

Department of Mathematical Sciences at Loughborough University
1. The Hypercube
How to build the 4 dimensional analogue of the cube. Includes movies of a spinning hypercube.
2. An ``Inflated Hypercube''
The hypercube may be though of as a crude approximation to the hypersphere. By inserting new vertices into the edges of a hypercube, it may be ``inflated'' to give a better
approximation, with more points lying on the surface of the corresponding hypersphere.
3. Hyper-torus
Adding together three vectors rotating in 4-space with different frequencies and amplitudes produces a trajectory along the surface of a hyper-torus.
4. How the models were produced
Details of the maths needed to model the structures, and how to turn the numbers into an animation.
Useful references on higher dimensional topics

Traversable Wormholes

by Michael Clive Price
Since 1985 there has been much theoretical progress on traversable wormholes. At first they were thought to enable time travel, so not
taken seriously. More recent work rules out time travel and associated paradoxes, but still permits faster-than-light travel. This article
explores some of the implications traversable wormholes have on the expansion of civilisations through the universe.

a point event in spacetime, Geometry of the light cone
Jack Sarfatti, 1995

Flatland - A Romance of Many Dimensions

by Edwin A. Abbott (1884) A true classic of hyperdimensionality. Inspiration for Rudy Rucker
This Work is Dedicated
By a Humble Native of Flatland
In the Hope that
Even as he was Initiated into the Mysteries
Of THREE DIMENSIONS
Having been previously conversant
With ONLY TWO
So the Citizens of that Celestial Region
May aspire yet higher and higher
To the Secrets of FOUR FIVE or EVEN SIX Dimensions
Thereby contributing
To the Enlargment of THE IMAGINATION
And the possible Development
Of that most and excellent Gift of MODESTY
Among the Superior Races
Of SOLID HUMANITY

The Theory of Evolutionary Process of Arthur M. Young

by Frank Barr
According to Young (1976a; 1980), the seven stages of process represent the seven topological distinctions possible with the torus, the most complex natural topological entity. The torus is a self-referential "time-structure" with numerous unique properties such as:
1) composition from two rotating "perpendicular circularities";
2) the shape of a vortex, an entity which is consubstantial with its matrix--i.e., the only means by which self-sustained motion can
exist in a given medium;
3) the same volume formula, 2pi²R³, as the Einstein-Eddington universe, the so-called hypersphere.
4) a universal distribution, occurring with photons and particles through the cellular centriole to the universal hypersphere;
5) the ability to reconcile the continuum of relativity and the discreteness of quantum theory;
6) the means to explain the ancient puzzle of "free will in a universe run by God" or how there can be self-determined entities in
the continuum; and
7) seven topological distinctions--(i.e., a map drawn on the surface of a torus requires seven colors in order for all bordering
countries to be distinguished by differences in color).

Relativity and Faster Than Light Travel

1995 by John H Kim Faster-than-light travel between star systems is a staple of much
science fiction. SF authors thus come up with various pseudo-scientific
explanations for it. Consequently, there is a lot of confusion about the
Theory of Relativity. This is only natural - it is a very complicated
theory which even physicists often have trouble with.

A Structured World of Liquid And Foamy Ether

An article on Theoretical Physics by Peter Hahn

The Warp Drive: Hyper-Fast
Travel Within General Relativity

Miguel Alcubierre

It is shown how, within the framework of general relativity and without the introduction of wormholes, it is possible to
modify a spacetime in a way that allows a spaceship to travel with an arbitrarily large speed. By a purely local expansion
of spacetime behind the spaceship and an opposite contraction in front of it, motion faster than the speed of light as
seen by observers outside the disturbed region is possible. The resulting distortion is reminiscent of the ``warp drive'' of
science fiction. However, just as it happens with wormholes, exotic matter will be needed in order to generate a distortion
of spacetime like the one discussed here.

A popular work which describes nineteenth century views on the subject of the fourth dimension is to be found in a work of fiction
called "Flatland" by E.A. Abbot (1884). This is a story about a being who has spent his entire life in a country that exists in two
dimensions. He has no idea about dimensions higher than the one on which he lives, himself being a two dimensional shape. The main
character is simply a square with eyes and a mouth on one of his vertices.

Society for the Advancement of Autodynamics

Autodynamics is a superset of Special Relativity. Among its implications are: the
ability to describe important experimental data that Special Relativity cannot (e.g., muon decay, nucleus-nucleus collision,
proton-proton annihilation), the theoretical lifting of the light speed barrier (including an outline of an experiment for creating
faster-than-light-speed photons).

Diffential Topology

Here are a few essays regarding manifolds. We address questions relating to their differentiable structure (and analytic structure) as
well as to their geometry.
Thinking about the definition of a manifold
What is the gradient (in differential topology)?
Is the smooth image of a manifold still a manifold? (no)
Review of the "long line" (the imposter manifold), along with some questions.
Deriving the equations of a torus.
Can you determine analytic functions on a manifold from the values on a set with an accumulation point? (no -- read to see djr mix up
results from complex analysis with real manifolds.)
Are most manifolds hyperbolic?
Finding a manifold with boundary RP^n
Classification of 4-dimensional manifolds (up to homeo- or diffeo-morphism), and applications to mathematical physics.

Arthur M.Young

inventor of the Bell Helicopter, cosmologist and author of The Reflexive Universe and The Geometry of Meaning,
addresses issues in physics, mathematics, consciousness and evolution. Learn about ongoing work to extend the theory into new areas from medicine, cognitive science, brain research and cellular biology to developmental psychology, problem solving and organizational planning.

Student of Hyperspace

What you will find on the pages linked to this one are a series of computer generated
projections of analogs of 3 of the 5 platonic solids in 4-space. The remaining 2 are in the
works. In addition there is a projection of a regular polytope that exists only in 4-space.
If you are wondering what I mean by hyperspace, I am referring to a Euclidian space of
more than 3 dimensions. Can I stand in my office and point in the direction of the 4th
dimension, No. Neither can I deny it's existance.

GEOMETRY

The Flat Torus in the Three-Sphere

One of the most interesting surfaces in four-dimensional space is the Flat Torus in the Three-Sphere.
To see the changing three-dimensional shadows created as this object completes a rotation in four-dimensional space, select any
point in the image below to download an animation. Thomas Banchoff's Project List

4Dice Project A Glimpse into the Fourth Dimension

Center for Innovative Computer Applications
An animation of four-dimensional dice

The Geometry Junkyard

Many-dimensional Geometry
A reference page

The Geometry Forum

The Geometry Forum is an electronic community focused on geometry and math education based at Swarthmore college.
Multimedia Documents

The Topological Zoo

It is a visual dictionary of surfaces and other
mathematical objects, consisting primarily of movies, still images and interactive pictures.
Special Exhibits:
Higher Dimensional Objects,
Knots and Links,
Fractals,
Hyperbolic Geometry,

HYPERMEDIA

Hypertext and Critical Theory

George P. Landow

Navigation in Hyperspace and Cognitive Representation

This page is being developed during the Cognitive Ergonomics course CO440 of Cognitive Science at the Nijmegen University, The Netherlands. The subject is on how people build
up mental representations of information collected in a hypermedia tour.

described by Vannevar Bush in his seminal article
"As We May Think," the Memex is the protoypical
hypermedia machine. Although never actually built, the
Memex had all the features now associated with the
multimedia computer workstation including: hyperlinked
text and images (microfiche filing system), networking
capabilities (via broadcast television), display terminal
(television screen), keyboard for inputing text, and data
storage (electromagnetic memory cards).

Vannevar Bush, the US Defense Department's most revered engineer during World War II, was the key computer
scientist to make the leap to the larger issues of information technology. In his seminal article, "As We May Think",
written in 1945 for the Atlantic Review, he forecast the future of hypermedia with his visionary Memex, the
prototypical multimedia workstation that influenced generations of knowledge pioneers.

Hypertext Consciousness

Mark Amerika (1995)
What happens when HTC is teleported through cyberspace? How can we reconfigure our
conceptions of authorship so that they allow for a new breed of writers called cyborg-narrators and what will these cyborg-narrators do
once they enter virtual reality?

Hypertext and Hypermedia -- A Subject Catalogue

and general index

realtime visualisation of the structure of a set of web pages

The hyperspace system allows a user to create a realtime visualisation of the structure of a set of web pages whilst browsing through them. hyperspace builds upon two strands of research within the Advanced Interaction Group at Birmingham: firstly, visualisation of complex
interacting systems (Hyper/Narcissus), and secondly, communications architectures to support multi-agent systems (cameo).
hyperspace is highly dynamic and can be extensively tailored and extended through its user and programming interfaces. The system is not
restricted to visualising hypertext structures either; it can be used for other data too.

Hypertext Places

Useful WWW sites regarding hypertext, hypermedia, and world wide web.

Introductions to Hypertext
Bibliographic Resources
History of Hypertext
Authoring Hypertext
Hypertext and Literary Theory
Hypertext Publishers
Some Interesting Examples
World Wide Web
Other Sites of Note

Hypertext Terms

This is a glossary of terms used within the WWW project. In most cases, their use corresponds to conventional use in hypertext
circles.

INDEX AND METAPAGES

The Next Dimension

a hyperspace fan-page

The Deoxyribonucleic
Hyperdimension

"listen, there's a hell of a universe next door: let's go!" e.e.cummings
PHYSIC and PSYCHIC EXPERIENCES OF A HYPERSPATIAL NATURE

MISCELLANOUS

HEASARC

High Energy Astrophysics Science Archive Research Center,inline animations of supernovas and black holes

Toward a Science of Consciousness 1996 ("Tucson II")

What is consciousness?
The nature of our conscious experience has returned to the forefront of scientific interest. Representatives from philosophy,
neuroscience, psychology, cognitive science, medicine, physiology, biochemistry, physics, mathematics, ethnology, contemplative
studies and other fields are invited to a second major interdisciplinary conference on consciousness.